Some large deviation results for sparse random graphs
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Author
Contributions
- Hewlett-Packard Laboratories. - Contributor
Publication
1996 - Hewlett Packard, Bristol [England, England
Language
English
Word Count
3,750 words, Guess
Page Count
15 pages
Identifiers
- OCLC Control Number45803148
- Open LibraryOL17613355M
Description
Abstract: "We obtain a large deviation principle (LDP) for the relative size of the largest connected component in a random graph with small edge probability. The rate function, which is not convex in general, is determined explicitly using a new technique. As a corollary we present an asymptotic formula for the probability that the random graph is connected. We also present an LDP and related result for the number of isolated vertices. Here we make use of a simple but apparently unknown characterisation, wheich is obtained by embedding the random graph in a random directed graph. The results demonstrate that, at this scaling, the properties 'connected' and 'contains no isolated vertices' are not asymptotically equivalent. (At the threshold probability they are asymptotically equivalent.)."
Subjects
Series Statement
- [Technical report] / HP Laboratories Bristol. Basic Research Institute in the Mathematical Sciences -- HPL-BRIMS-96-22.
- BRIMS technical report -- HPL-BRIMS-96-22.
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